Simplify the Expression: a¹⁰ × b⁵ × a⁻² × b³

Simplify the following problem:

$a^{10}\times b^5\times a^{-2}\times b^3=$

Begin by applying the distributive property of multiplication and arrange the algebraic expression according to like bases:

$a^{10}\cdot a^{-2}\cdot b^5\cdot b^3$

From here on we will no longer indicate the multiplication sign, instead we will simply place terms next to each other.

Note that we need to multiply terms with identical bases, hence we'll apply the appropriate power rule:

$c^m\cdot c^n=c^{m+n}$

This rule can only be used to calculate multiplication between terms with identical bases,

In this problem, there is also a term with a negative exponent, but this doesn't pose an issue regarding the use of the aforementioned power rule. In fact, this power rule is valid in all cases for numerical terms with different exponents, including negative exponents, rational exponents, and even irrational exponents, etc.,

Let's apply it to the problem:

$a^{10}a^{-2}b^5b^3=a^{10-2}b^{5+3}=a^8b^8$

We dealt with the terms with equal bases separately, meaning separately from the terms with the bases $a$ and $b$

Therefore the correct answer is D.